Non-Walker Self-Dual Neutral Einstein Four-Manifolds of Petrov Type III

Abstract

The local structure of the manifolds named in the title is described. Although curvature homogeneous, they are not, in general, locally homogeneous. Not all of them are Ricci-flat, which answers an existence question about type III Jordan-Osserman metrics, raised by Diaz-Ramos, Garcia-Rio and Vazquez-Lorenzo (2006).

47 pages; a reference and a grant number were added

References in corpus (3)

• The geometry of modified Riemannian extensions
• Connections with skew-symmetric Ricci tensor on surfaces
• Walker's theorem without coordinates

Cited by in corpus (9)

• The geometry of modified Riemannian extensions
• Noncompactness and maximum mobility of type III Ricci-flat self-dual neutral Walker four-manifolds
• Gauge theory on projective surfaces and anti-self-dual Einstein metrics in dimension four
• Half conformally flat gradient Ricci almost solitons
• Four-dimensional neutral signature self-dual gradient Ricci solitons
• Affine projective Osserman structures
• Compact Osserman manifolds with neutral metric
• Higher-dimensional Osserman metrics with non-nilpotent Jacobi operators
• Projective affine Ossermann curvature models